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January 8th, 2016, 11:02 AM  #1 
Newbie Joined: Dec 2015 From: pakistan Posts: 5 Thanks: 0  Finding the area of parallelogram? Sides given in linear equations
"Find the area of a parallelogram bounded by the yaxis, the lineâ€‰x =3, the lineâ€‰f(x)=1+2x, and the line parallel toâ€‰f(x)â€‰passing throughâ€‰(2, 7)." Okay, so a few things I don't understand here. I'm not a native English speaker, so please allow me some leeway. What does it mean for a parallelogram to be bounded by the yaxis? From the above, one line is vertical (x=3) second line is f(x)=2x+1, third line and parallel to this would be 7=2(2)+b b=3 or g(x)=2x+3 So now we have x=3,2x+1 and 2x+3 The area of a paralellogram is height*base. Height can be found by the distance between any two points on the two parallel lines. For line g(x) we already have 2,7. at x=3 f(x) would return 5 so now we have 2,7 and 2,5 using d=root((22)^2 + (75)^2) we get 2 Now we have height=2. How do I find the base now? I mean, we are just given two equations of the line; how do I find where the lines begin and where they end? (i.e the domain). Can somebody help me out with this? Here's the graph https://www.desmos.com/calculator/n8gv0l2vx8 Last edited by skipjack; January 8th, 2016 at 02:15 PM. 
January 8th, 2016, 11:43 AM  #2 
Global Moderator Joined: May 2007 Posts: 6,787 Thanks: 708 
The side parallel to x=3 is the y axis, which is x=0. Therefore, the base is 3 wide, so the area is 6.


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area, equations, finding, linear, linear algebra, parallelogram, sides 
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